The initial wave function is chosen such that after Charlie and Debbie each perform a measurement of the respective half of entangled spin along \(z\)  axis, from Alice's or Bob's perspective, it becomes (see Eqs.(5)-(9) in  [1]}):
\(\begin{split}|\Psi \rangle &= - \frac{1}{\sqrt{2}}\sin \frac{\theta }{2}(|00\rangle _{L_1}|00\rangle _{L_2} + |11\rangle _{L_1}|11\rangle _{L_2})\\&+\frac{1}{\sqrt{2}}\cos \frac{\theta }{2}(|00\rangle _{L_1}|11\rangle _{L_2} - |11\rangle _{L_1}|00\rangle _{L_2}),\end{split}\) 
